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R. B. Francoeur, “Fever and Depressive Affect Clarify a Common Cancer Cluster (Pain-Sleep Problems-Fatigue/ Weakness) in an Outpatient Survey: A New Method for Moderated Regression Improves Detection of Interactions and Synergistic Relationships,” Under Review.

ABSTRACT:
Multicollinearity constitutes shared variation among predictors that inflates standard errors of regression coefficients. Several years ago, it was proven that the common practice of mean centering in moderated regression cannot alleviate multicollinearity among variables comprising an interaction, but merely masks it. Residual centering (orthogonalizing) is unacceptable because it biases parameters for predictors from which the interaction derives, thus precluding interpretation of moderator effects. I propose and validate residual centering in sequential re-estimations of a moderated regression—sequential residual centering (SRC)—by revealing unbiased multicollinearity conditioning across the interaction and its related terms. Across simulations, SRC reduces variance inflation factors (VIF) regardless of distribution shape or pattern of regression coefficients across predictors. For any predictor, the reduced VIF is used to derive a lower standard error of its regression coefficient. A cancer sample illustrates SRC, which allows unbiased interpretations of symptom clusters. SRC can be applied efficiently to alleviate multicollinearity after data collection and shows promise for advancing synergistic frontiers of research.